TY - JOUR
T1 - The Set of Linear Time-Invariant Unfalsified Models with Bounded Complexity is Affine
AU - Mishra, Vikas Kumar
AU - Markovsky, Ivan
PY - 2021/9
Y1 - 2021/9
N2 - We consider exact system identification in the behavioral setting: given an exact (noise-free) finite time series, find the set of bounded complexity linear time-invariant systems that fit the data exactly. First, we modify the notion of the most powerful unfalsified model for the case of finite data by fixing the number of inputs and minimizing the order. Then, we give necessary and sufficient identifiability conditions, i.e., conditions under which the true data generating system coincides with the most powerful unfalsified model. Finally, we show that the set of bounded complexity exact models is affine: every exact model is a sum of the most powerful unfalsified model and an autonomous model with bounded complexity.
AB - We consider exact system identification in the behavioral setting: given an exact (noise-free) finite time series, find the set of bounded complexity linear time-invariant systems that fit the data exactly. First, we modify the notion of the most powerful unfalsified model for the case of finite data by fixing the number of inputs and minimizing the order. Then, we give necessary and sufficient identifiability conditions, i.e., conditions under which the true data generating system coincides with the most powerful unfalsified model. Finally, we show that the set of bounded complexity exact models is affine: every exact model is a sum of the most powerful unfalsified model and an autonomous model with bounded complexity.
UR - http://www.scopus.com/inward/record.url?scp=85098782668&partnerID=8YFLogxK
U2 - 10.1109/TAC.2020.3046235
DO - 10.1109/TAC.2020.3046235
M3 - Article
VL - 66
SP - 4432
EP - 4435
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 9
ER -